Achieves 1,000x speedups in Bayesian inverse problems by replacing repeated MCMC sampling with one-step preconditioned generative transport.
March 17, 2026
Original Paper
Preconditioned One-Step Generative Modeling for Bayesian Inverse Problems in Function Spaces
arXiv · 2603.14798
The Takeaway
It maps reference Gaussian noise directly to posterior samples in milliseconds while maintaining the regularity needed for PDE-based problems. For engineers and scientists solving inverse problems, this bypasses the massive computational bottleneck of repeated forward-model evaluations required by traditional MCMC.
From the abstract
We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime based on one-step generative transport. Building on the Mean Flows, we learn a fully conditional amortized sampler with a neural-operator backbone that maps a reference Gaussian noise to approximate posterior samples. We show that while white-noise references may be admissible at fixed discretization, they become incompatible with the function-space limit, leading to instability in inference for Ba